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# A car traveling at a certain constant speed takes 2 seconds

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SVP
Joined: 11 Sep 2015
Posts: 1977

Kudos [?]: 2858 [1], given: 364

Re: A car traveling at a certain constant speed takes 2 seconds [#permalink]

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13 Dec 2017, 07:23
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A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling?

A. 71.5
B. 72
C. 72.5
D. 73
E. 73.5

GIVEN: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour.
Let x = the car's speed

We can write: (travel time at x km per hour) = (travel time at 75 km per hour) + 2 seconds
Since the speeds are in km per HOUR, let's rewrite 2 seconds as 2/3600 hours (since there are 3600 second in one hour)

We get: (travel time at x km per hour) = (travel time at 75 km per hour) + 2/3600 hours
Or: (travel time at x km per hour) = (travel time at 75 km per hour) + 1/1800 hours

Travel time = distance/speed

We get: 1/x = 1/75 + 1/1800 hours
The least common multiple of the denominators is 1800x, so....
Multiply both sides by 1800x to get: 1800 = 24x + x
Simplify: 1800 = 25x
Solve: x = 1800/25 = 72

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Kudos [?]: 2858 [1], given: 364

Intern
Joined: 16 Jul 2016
Posts: 33

Kudos [?]: 10 [1], given: 2

A car traveling at a certain constant speed takes 2 seconds [#permalink]

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15 Dec 2017, 09:39
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$$rate * time = distance$$

rate and time are inversely proportional. So assuming the distance stays the same, doubling the time will half the rate. multiplying the time by 3/2 will result in a rate 2/3 as much.

75 * (1/75) = 1

The car goes 75 km per hour for 1/75 of an hour so for (3600/75)=48 seconds.

When the car takes two seconds longer it takes 50 seconds. The time increased by a factor of (25/24). The rate must therefore be multiplied by (24/25).

$$75(\frac{24}{25})=72$$

Kudos [?]: 10 [1], given: 2

A car traveling at a certain constant speed takes 2 seconds   [#permalink] 15 Dec 2017, 09:39

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